After winning all of the national competitions in Uruguay, he was awarded a full scholarship from the Peabody Conservatory of the Johns Hopkins University and the Organization of American States to study with Leon Fleisher in 1973.

Graf has performed concertos by Bach, Haydn, Mozart, all five and the Triple by Beethoven, Brahms, Mendelssohn, Liszt, Franck, Tchaikovsky, Grieg, Rachmaninoff, Ravel, Poulenc, Gershwin, De Falla, Turina, Shostakovich, and Lee Hoiby.

[21] Graf taught for fourteen years at the Peabody Preparatory, became chairman of the piano department and received the Director's Award for Outstanding Teaching.

Graf is Founder and Artistic Director of the Festival Internacional de Colonia in Uruguay,[26] Directed the International Piano Series in Charleston and the Young Artist Series in the Piccolo Spoleto Festival and co-founded Music Fest Perugia in Italy.

He has been awarded a Fellowship from the Aspen Institute Executive Seminar, the Music Fellowship from the South Carolina Arts Commission, Career Grants from the Charles Del Mar and Astral Foundations, and the Immigrant Achievement Award in 2000 from the American Immigration Law Foundation.